These calculators (and any calculators) can be effectively
used to numerically solve differential equations using any
of the usual methods. We will implement Euler's method,
Heun's method (improved Euler's) and Runge-Kutta. The
methods will be implemented in a number of ways, ranging
from simple use of the calculators to more sophisticated
use of their programming capabilities.

The simplest method is to type in the steps of the
algorithm one at a time. The steps can be repeated
easily by using the key sequence [2nd][ENTRY], which
brings the previous command up for editing and use.
Pressing [2nd][ENTRY] twice goes back two commands,
etc.

Euler's Method

As an example, we use this method with Euler's method
to numerically solve the equation
y'=sin(x)-y
with initial conditions y(0)=1 and step size
h=0.25.

For any more than a very few steps it is worth using the
simple programming ability of the TI-8x to run a loop. Enter
the program editor by pressing the [PRGM] key. Either edit
an existing program or create a new program.